Frequency locking

As we further change the parameter R, the hysteresis interval ends (the invariant circle stops existing) and the only attractor is the stable periodic frequency locked solution N. Both sides of the unstable manifold of the sad e-type frequency locked solution are attracted to N (Point G, inset 2e). 

The mechanism of these transitions is nontrivial and has been discussed in detail elsewhere Q, 12) it involves the development of a homoclinic tangencv and subsequently of a homoclinic tangle between the stable and unstable manifolds of the saddle-type periodic solution S. This tangle is accompanied by nontrivial dynamics (chaotic transients, large multiplicity of solutions etc.). It is impossible to locate and analyze these phenomena without computing the unstable, saddle-tvpe periodic frequency locked solution as well as its stable and unstable manifolds. It is precisely the interactions of such manifolds that are termed global bifurcations and cause in this case the loss of the quasiperiodic solution. 

Fast Fourier transform (FFT) A procedure for carrying out Fourier transformation at high speed, with a minimum of storage space being used. Field frequency lock The magnitude of the field Bq is stabilized by locking onto the fixed frequency of a resonance in the solution, usually of the solvent. 

As mentioned above, in an ENDOR experiment the rf field is swept while the static magnetic field is held at a constant position in the EPR spectrum. For slow sweep rates and narrow EPR lines a device would be desirable which is able to stabilize the ratio of the microwave frequency to the static magnetic field. The applicaiton of a commercially available field/frequency lock system is restricted to a region of 6 mT about the DPPH resonance field33). In metal complexes with strongly anisotropic EPR spectra, however,... 

For quantitative estimation, a sealed reusable capillary tube, with a known quantity of sodium salt of trimethylsilyl propionic acid (TSP) dissolved in 35 pi of D20, is inserted into the NMR tube while obtaining NMR spectra. The internal standard TSP is used as a chemical shift reference as well as a quantitative standard for the estimation of metabolites, and D20 is used as the field-frequency-lock . Spectra are acquired at room temperature. Typical spectra acquired at room temperature of human bile and standard glycine- and taurine-conjugated BAs are shown in Fig. 5.4.16. 

Beyond the scope of this article, Anderson explains the operation of the gyroscope in intimate detail and describes two problems that have proved most vexing to manufacturers of the rtng-laser gyroscope, namely, frequency locking at low rotation rates and the bias effect. Improvements In this instrument are expected in the relatively near future heeause of what scientists have recently learned pertaining to the phenomenon of optical phase conjugation. 

This measure can be used to characterize the various forms of frequency locking between the two modes. With varying feedback delay T and varying slope a of the open loop feedback curve, Fig. 12.11 shows how the two oscillatory modes can adjust their dynamics and attain states with different rational relations (p q) between... 

One aspect of the experimental conditions under which these spectra were obtained is important to understand so that the spectra can be rationally interpreted. For solubility and stability purposes, peptides are generally dissolved in buffered water. Recall from Chapter 3 that compounds prepared for NMR experiments are almost always dissolved in deuterated solvents. The need for deuterated solvents is so that the spectrometer can remain stable for the duration of the experiment by way of the field/frequency lock. The lock signal comes from the deuterium NMR signal of... 

A sample for NMR spectroscopy can be taken from several stages of the sample preparation path (see Chapter 9) (14-19-28). Preferably, this would be a 5-10-mL portion of extract or of aqueous or organic liquid. Common to all these solutions is the large molar excess of H in the solvent compared to the amount of 111 in the possible target chemicals. This yields an intense solvent (e.g. H20, CH2C12) resonance in the 111 NMR spectrum, making the trace analysis difficult or even impossible. A usual procedure to avoid this problem is to replace the protonated solvent (e.g. H20) with the corresponding deuterated solvent (D20). Deuter-ated solvents are also used for the field-frequency lock of the spectrometer. 

Abstract. We present a review of the helium spectroscopy, related to transitions between 23S and 23P states around 1083 nm. A detailed description of our measurements, that have produced the most accurate value of the 23Po — 23Pi fine structure interval, is given. It could produce an accurate determination (34 ppb) of the fine structure constant a. Improvements in the experimental set up are presented. In particular, a new frequency reference of the laser system has been developed by frequency lock of a 1083 nm diode laser to iodine hyperfine transitions around its double of frequency. The laser frequency stability, at 1 s timescale, has been improved of, at least, two orders of magnitude, and even better for longer time scales. Simultaneous 3He —4 He spectroscopy, as well as absolute frequency measurements of 1083 nm helium transitions can be allowed by using the Li-locked laser as frequency standard. We discuss the implication of these measurements for a new determination of the isotope and 23 5 Lamb shifts. 

The 500-MHz, H-n.m.r. spectra were recorded with a Bruker WM-500 spectrometer operating in the pulsed, Fourier-transform mode and equipped with a Bruker Aspect2000 computer having an 80k memory-capacity. The D resonance of D20 was used as the field-frequency lock-signal. The spectra were obtained by using a 90° pulse-width, and accumulated into 16k addresses with an acquisition time of... 

Nitrogen-15 nmr spectra were obtained at 9.12 and 20.72 MHZ on spectrometers using external time-share, field-frequency lock. Details of the spectrometer modifications are published elsewhere (19). 

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